A. Field of the Invention
This invention relates to human motion analysis and, more particularly, to analysis of joint forces and moments using nonlinear feedback in a forward dynamic simulation.
B. Description of Background Art
In the study of human motion, inverse dynamics analysis is conventionally used to estimate joint forces and joint moments. In a conventional inverse dynamics analysis, joint forces and joint moments are calculated from the observation of segmental movement. Inverse dynamics analysis is conventionally applied to biomechanics problems because the internal forces of human joints cannot be readily measured. Segmental movements, however, can be measured and joint angles can be inferred from the measured displacement to determine the corresponding joint forces and torques.
A problem with using inverse dynamics in the study of human motion is the error caused by calculating higher order derivatives to determine joint forces and joint moments. Methods for using inverse dynamics concepts in biomechanics are well developed if the input signals are noise-free and the dynamic model is perfect. Experimental observations, however, are imperfect and contaminated by noise. Sources of noise include the measurement device and the joint itself. Inverse dynamics methods for calculating joint moments require the calculation of higher order derivatives of the experimental observations. Specifically, the angular acceleration term is the second derivative of the joint angle and the linear acceleration is the second derivative of the center of mass acceleration. Numerical differentiation of the experimental observations amplifies the noise. The presence of high frequency noise is of considerable importance when considering the problem of calculating velocities and accelerations. The amplitude of each of the harmonics increases with its harmonic number: velocities increase linearly, and accelerations increase proportional to the square of the harmonic number. For example, second order differentiation of a signal with high frequency noise ω can result in a signal with frequency components of ω2. The result of this parabolic noise amplification is erroneous joint force and joint moment calculations.
Although techniques exist for filtering the noise, filtering is difficult and time-consuming because much analysis is required to separate the true signal in the biomechanical data from the noise. For example, low-pass filtering is commonly used to reduce high frequency errors. A difficulty in low-pass filtering, however, is the selection of an optimal cutoff frequency fc. Because there is no general solution for selecting optimal filter parameters, filtering techniques often produce unreliable results.
Optimization-based approaches have been proposed to estimate joint forces and joint moments without the errors associated with performing a conventional inverse dynamics analysis. Unlike inverse dynamics, optimization-based methods do not require numerical differentiation. However, the application of optimization-based solutions is limited because the methods are computationally expensive, are not guaranteed to converge, and are generally too complex to implement.
Another problem with using inverse dynamics for analyzing human motion is that the inverse technique lacks the capability to predict the behavior of novel motions. In inverse dynamics, forces and moments are calculated from observed responses. The prediction of novel motions involves calculating the response expected from the application of forces and moments. An inverse dynamics analysis lacks predictive capability because forces and moments are calculated rather than the expected response from the application of those forces and moments.
What is therefore needed is a computationally efficient system and method that: (1) estimates joint forces and joint moments without the errors due to higher order derivatives; (2) does not require closed form, whole body analysis; and (3) is useful for predicting the behavior of human motions.